A new twist on the Carleson operator

Must the Fourier series of an L^2 function converge pointwise almost
everywhere? In the 1960's, Carleson answered this question in the
affirmative, by studying a particular type of maximal singular integral
operator, which has since become known as the Carleson operator. In the
past 40 years, a number of important results have been proved for
generalizations of the original Carleson operator. In this talk we will
describe new joint work with Po Lam Yung that introduces curved
structure to the setting of Carleson operators.